Produces a generalized linear model family object with any power variance function and
any power link. Includes the Gaussian, Poisson, gamma and inverse-Gaussian families as
special cases.

USAGE

tweedie(var.power = 0, link.power = 1-var.power)

OPTIONAL ARGUMENTS

var.power

index of power variance function

link.power

index of power link function. link.power=0 produces a log-link. Defaults to
the canonical link, which is 1-var.power.

VALUE

A family object, which is a list of functions and expressions used by glm and gam
in their iteratively reweighted least-squares algorithms. See family.object in
the S-Plus help for details.

DETAILS

This function provides access to a range of generalized linear model response
distributions which are not otherwise provided by S-Plus, or any other package for that
matter. It is also useful for accessing distribution/link combinations which are
perversely disallowed by S-Plus, such as Inverse-Gaussion/Log or Gamma/Identity.

Let mi = E( yi)
be the expectation of the ith response. We assume that

miq = xiTb, var( yi) = fmip

where xi is a vector of covariates and b is a vector of regression cofficients, for some f, p and q. This family is specified by var.power
= p and link.power = q. A value of zero for q is interpreted
as log(mi) = xiTb.

The variance power p characterizes the distribution of the
responses y. The following are some special cases:

p

Response distribution

0

Normal

1

Poisson

(1, 2)

Compound Poisson, non-negative with mass at zero

2

Gamma

3

Inverse-Gaussian

> 2

Stable, with support on the positive reals

The name Tweedie has been associated with this family by Jørgensen in
honour of M. C. K. Tweedie.

REFERENCES

Tweedie, M. C. K. (1984). An index which distinguishes between some important
exponential families. In Statistics: Applications and New Directions. Proceedings of
the Indian Statistical Institute Golden Jubilee International Conference. (Eds. J. K.
Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.